Soliton solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas

Abstract

In this paper, we extended the improved \(\tan(\phi/2)\)-expansion method (ITEM) and the generalized \(G'/G\)-expansion method (GGEM) proposed by Manafian and Fazli (Opt. Quantum Electron. 48, 413 (2016)) to construct new types of soliton wave solutions of nonlinear partial differential equations (NPDEs). Moreover, we use of the improvement of the Exp-function method (IEFM) proposed by Jahani and Manafian (Eur. Phys. J. Plus 131, 54 (2016)) for obtaining solutions of NPDEs. The merit of the presented three methods is they can find further solutions to the considered problems, including soliton, periodic, kink, kink-singular wave solutions. This paper studies the quantum Zakharov-Kuznetsov (QZK) equation by the aid of the improved \(\tan(\phi/2)\)-expansion method, the generalized \(G'/G\)-expansion method and the improvement of the Exp-function method. Moreover, the 1-soliton solution of the modified QZK equation with power law nonlinearity is obtained by the aid of traveling wave hypothesis with the necessary constraints in place for the existence of the soliton. Comparing our new results with Ebadi et al. results (Astrophys. Space Sci. 341, 507 (2012)), namely, \(G'/G\)-expansion method, exp-function method, modified F-expansion method, shows that our results give further solutions. Finally, these solutions might play an important role in engineering, physics and applied mathematics fields.